---
title: "Is a hydraulic jump stilling basin required?"
subject: "Hydropower Engineering"
chapter: 4
key: "semester_7/hydropower_engineering:stilling-basin-required-check-100cumec"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/stilling-basin-required-check-100cumec
site: BCT Engineering
---

# Is a hydraulic jump stilling basin required?

Hydropower Engineering · Chapter 4: Headworks of Storage Plants

- Asked in: 2081 Baishakh, 6 marks
- Video: [Design concepts of Stilling Basin(Nepali) !Hydropower Engineering ! Part-1! Hydrolic jump problem](https://www.youtube.com/watch?v=wH3LDTQM5vs) — RS EDUCATION
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/stilling-basin-required-check-100cumec
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-4

## Question

Check whether a hydraulic jump type stilling basin is required or not for a hydropower project. Given that the discharge is 100 cumec flowing through a 10 m long overflow spillway. The height of the spillway crest is 30 m from the downstream bed with a slope of river as 1 in 500, Manning's roughness coefficient is 0.018 and coefficient of discharge is 0.75.

## Short answer

Required. Conjugate depth y2=6.97 m; tailwater depth 2.75 m is much smaller. Use USBR Type II basin, depress floor, length approx 30 m.

## Answer

A hydraulic jump basin is needed if the natural tail water depth is **less than** the conjugate (sequent) depth $y_2$ needed to hold the jump at the toe.

**Given**: $Q=100$ m³/s, spillway width $B=10$ m, height of crest above d/s bed $P=30$ m, $S_0=1/500$, $n=0.018$, $C_d=0.75$. The river downstream is assumed rectangular with the same width.

#### Step 1: Unit discharge and head
$$
q=\frac{100}{10}=10\ \text{m}^3/\text{s/m},\qquad 10=\tfrac23(0.75)(4.429)H^{3/2}\Rightarrow H=2.73\ \text{m}
$$

#### Step 2: Depth and velocity at the toe
$E=P+H=30+2.73=32.73$ m (losses neglected).
$$
y_1+\frac{q^2}{2gy_1^2}=32.73\Rightarrow y_1=0.397\ \text{m},\quad V_1=25.2\ \text{m/s},\quad Fr_1=12.76
$$

#### Step 3: Required tail water (sequent depth)
$$
y_2=\frac{y_1}{2}\left(\sqrt{1+8Fr_1^2}-1\right)=6.97\ \text{m}
$$

#### Step 4: Available tail water (Manning)
For the 10 m wide channel carrying 100 m³/s with $S_0=0.002$ and $n=0.018$:
$$
Q=\frac1nAR^{2/3}S_0^{1/2}\ \Rightarrow\ y_n=2.75\ \text{m}
$$
(Check: $A=27.5$ m², $R=1.77$ m, $Q=100.0$ m³/s.)

#### Step 5: Decision
$$
y_n=2.75\ \text{m}<y_2=6.97\ \text{m}\quad(y_n/y_2=0.39)
$$
The available tail water is much smaller than the required sequent depth, so the jump would be swept far downstream and the d/s bed would be scoured.

**Answer**: a stilling basin **is required**. The floor must be depressed (or a sill/baffle arrangement provided) to give a tail water depth of about $y_2=6.97$ m; since $Fr_1=12.76>4.5$ and $V_1>18$ m/s, a USBR Type II basin of length about $4.3y_2=30.0$ m is suitable.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. When is a hydraulic jump stilling basin required?
   A. When natural tail water depth is less than the sequent depth y2
   B. When tail water exceeds y2
   C. When Fr1 < 1
   D. When the slope is steep
   Answer: A. If the tail water cannot supply y2, the jump is swept away and the bed scoured. (Key point: Criterion)

2. What are the values of sequent depth and available tail water?
   A. y2 = 6.97 m required, yn = 2.75 m available
   B. y2 = 2.75 m, yn = 6.97 m
   C. Both 6 m
   D. y2 = 0.397 m, yn = 12.76 m
   Answer: A. y2 from the toe conditions is 6.97 m; Manning's normal depth is 2.75 m. (Key point: Required vs available)

3. Which basin suits Fr1 = 12.76 and V1 above 18 m/s?
   A. USBR Type II with chute blocks and dentated sill
   B. Type III with baffle blocks
   C. Type IV
   D. No basin
   Answer: A. For Fr1 > 4.5 and V1 > 18 m/s, Type II is used with length about 4.3 y2. (Key point: Basin type)

## Related in Hydropower Engineering

- [Hydraulic jump stilling basin at spillway toe](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Astilling-basin-hydraulic-jump-80cumec-2070) — Hydropower Engineering, chapter 4
- [Hydraulic jump stilling basin (25 m³/s/m)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Astilling-basin-25cumec-per-m-2074) — Hydropower Engineering, chapter 4
- [Hydraulic jump stilling basin (28 m³/s/m)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Astilling-basin-28cumec-per-m-2075) — Hydropower Engineering, chapter 4
- [Discharge through chute spillway ogee crest](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aspillway-chute-discharge-ogee-250m) — Hydropower Engineering, chapter 4
- [Minimum length of concrete apron of stilling basin](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Astilling-basin-apron-length-115cumec) — Hydropower Engineering, chapter 4
- [Discharge from hydraulic jump depths 1.5 m to 4 m](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Astilling-basin-hydraulic-jump-depth-change-120m) — Hydropower Engineering, chapter 4

## Related in other subjects

- [Discharge over overflow spillway](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aoverflow-spillway-discharge) — Hydro Power, chapter 6
- [Hydraulic jump definition and downstream Froude number](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-jump-what-is-and-froude-after-jump) — Hydraulics, chapter 9
- [Bump followed by hydraulic jump, find bump height](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aflow-over-bump-then-jump-v1-v3-y4-h) — Hydraulics, chapter 9, asked 2×
- [Jump at spillway toe; repelled and submerged jump](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ajump-at-toe-of-spillway-repelled-submerged) — Hydraulics, chapter 9